Asymptotic properties of branching processes in random environment

Authors
Guivarc'h, Y Liu, QS
Citation
Y. Guivarc'H et Qs. Liu, Asymptotic properties of branching processes in random environment, CR AC S I, 332(4), 2001, pp. 339-344
Citations number
11
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
332
Issue
4
Year of publication
2001
Pages
339 - 344
Database
ISI
SICI code
0764-4442(20010215)332:4<339:APOBPI>2.0.ZU;2-V
Abstract
Let (Z(n)) be a branching process in a random environment. If the process i n sub-critical or critical, we study the convergence rate of the survival p robability P(Z(n) > 0) as n --> infinity: if the process is supercritical, we give a necessary and sufficient condition for the convergence in L-P of the natural martingale, where p > 1 is given. (C) 2001 Academie des science s/Editions scientifiques et medicales Elsevier SAS.